Nigeria's Osimhen, who is Serie A's top scorer this season with 21 goals, has already missed this month's league games against Milan and Lecce due to a thigh strain.
In a post on their website, Napoli said Osimhen "worked separately" from the team during Tuesday's training session.
Giacomo Raspadori (23) is expected to lead the line against Milan in his place, with Argentine striker Giovanni Simeone (27) also sidelined due to a thigh issue.
Napoli beat Eintracht Frankfurt 5-0 on aggregate in the last 16 last month to reach the quarter-finals of the Champions League for the first time.
If they can get past Milan, they'll face either Inter or Benfica in the semi-finals and, given their league form, would be the favourite against both clubs.
However, confidence that they'll get to the next round decreased after their quarter-final opponents beat them 4-0 away from home in Serie A.
Such is their lead in the league that they still look all but certain to win their first Scudetto since 1990, but claiming glory in the Champions League will be more difficult, especially with Osimhen unable to play a part in the first leg of their upcoming tie.